theorem Th64:
  H is Sub_atomic iff H is atomic or H is negative &
  the_argument_of H is atomic
proof
  thus H is Sub_atomic implies H is atomic or H is negative & the_argument_of
  H is atomic
  proof
    assume
A1: H is Sub_atomic;
    per cases by A1;
    suppose
      H is atomic;
      hence thesis;
    end;
    suppose
A2:   ex G being LTL-formula st G is atomic & H = 'not' G;
      then H is negative;
      hence thesis by A2,MODELC_2:def 18;
    end;
  end;
  thus H is atomic or H is negative & the_argument_of H is atomic implies H is
  Sub_atomic
  proof
    assume
A3: H is atomic or H is negative & the_argument_of H is atomic;
    per cases by A3;
    suppose
      H is atomic;
      hence thesis;
    end;
    suppose
A4:   H is negative & the_argument_of H is atomic;
      then H = 'not' the_argument_of H by MODELC_2:def 18;
      hence thesis by A4;
    end;
  end;
end;
